Kjeldsen, who sits 34th in the Order of Merit, carded eight birdies in his round with the only blip a bogey at No. 17.
It was a very solid round. Im playing well, as I did last week at the Portugal Masters, said the 33-year-old Dane, who is looking for his first European Tour victory in five years. Theres still a long way to go this week but this is a good start.
Former U.S. Open champion Angel Cabrera, Englands Richard Finch, Ignacio Garrido of Spain and Peter Hanson of Sweden all trailed Kjeldsen after 6-under rounds of 65.
Sergio Garcia closed with three birdies to finish 5-under on his home course. Garcias father Victor is the pro at the Club de Campo del Mediterraneo.
Im taking advantage of the opportunities when they come. Its a very nice feeling playing at home. There has been a lot of buildup to it and its finally here and I was a little nervous this morning, said the Spaniard, who is looking for his first European win in three years. Scoring wise it was a good round but I know I need to play a little better.
Two-time Masters champion Jose Maria Olazabal was tied with Garcia and five other players to trail Kjeldsen by two strokes. Olazabal is playing in his second tournament since his latest comeback.
Englands Paul Casey (69) and Camilo Villegas (70) of Colombia were also in the running for the $448,628 first-place prize money.
The tournament was played while five-time major winner Seve Ballesteros was preparing to undergo a third operation Friday to remove the remaining parts of a cancerous tumor from his brain.
Madrids La Paz hospital said the 51-year-old Ballesteros was in stable, but serious, condition on Thursday.